Throughout this paper, we will often refer to the fundamental identity of time-frequency analysis, which is the fact that the Fourier transform corresponds to a rotation by 90 degrees of the time-frequency plane (see e.g. Lemma 3.1.1 on p. 39 of [1]}):
\(\mathcal {V}_\phi f (x,\omega ) = \mathrm {e}^{-2\pi \mathrm {i}x \omega } \mathcal {V}_{\mathcal {F}\phi } \mathcal {F}f (\omega ,-x), \qquad (x,\omega ) \in \mathbb {R}^2,\) 
